This Thesis describes and discusses the results obtained from observations of the astronomical objects Cygnus X-3 and the Crab Pulsar, made during 1981 and 1982 using the Very High Energy (VHE) Gamma Ray Astronomy Facility of the University of Durham. Following an introductory chapter, chapter two describes the observational technique used for the work (known as the 'Atmospheric Cerenkov Technique') and chapter three describes in some detail the design, construction and operation of the equipment. Chapter four summarises the data taken during the course of the observations, whilst chapter five describes the analysis techniques used in the examination of this data. Chapter six presents the results derived from these analyses and, finally, chapter seven discusses their implications, both for the objects themselves and for the field of Astrophysics generally. Unless otherwise stated, the Author has either been principally responsible for, or has played an important part in the production of, all the work reported in this Thesis.